i don't know where i saw the question is does this expression (Cesaro sum ??) make sense for big lambda and positive delta(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \sum_{n \le \lambda } (1- \frac{n}{\lambda})^{\delta} \mu (n)=S( \lambda , \delta) [/tex]

for finite lambda the S is finite the question is what would happen as lambda goes to infinity ?, does the sum converge in the sense that for lambda big.

[tex] S \sim A+ O( \lambda ^{-b} [/tex] (b a positive real number)

and the same for

[tex] \sum_{n \le \lambda } (1- \frac{n}{\lambda})^{\delta} \Lambda (n)=S( \lambda , \delta) [/tex]

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# Does this expression make sense.

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